Mesh Decimation using Probabilistic Quadrics

CGAL currently supports the decimation of triangular meshes using two distinct strategies: Lindstrom-Turk and Garland-Heckbert. These strategies assign a cost to each edge collapse so that edges can be iteratively collapsed in order of least cost until a condition is met.

Our focus is on the latter of the two strategies, which uses quadrics at each vertex to calculate a cost. The paper Fast and Robust QEF Minimization using Probabilistic Quadrics explores the use of probabilistic - as opposed to classic - quadrics and shows that in many use cases, including but not limited to mesh decimation, probabilistic quadrics give better results, are more robust and about as efficient as classical quadrics.

The aim of this project is to introduce support for probabilistic quadrics in the context of mesh decimation in CGAL, which would improve the library's capability to quickly generate highly desirable mesh simplifications.